How to simplify/clean up a mesh?
Generally I would advise not worrying about topology when you model. Clean topology can be essential and a mark of good modeling skills but its much better to model first and retopologise later. 

The reason being unless you have decided exactly what your final form will be, topology will be simply impossible to predict. 

You can waste a ton of time being a perfectionist in 3d graphics, so it is better to keep it simple focus on just modeling the form you want. After you finish you can always either edit your mesh to fix topology problems or you can create new topology using the snap to surface or wrap skin modifier tools. 

There are of course cases where bad topology can get in the way of modeling the object in that case you either edit the mesh to correct these problems or retopologise it. There is the remesher as you pointed but quickly you will find there is no golden tool in any 3d graphics app that will clean up your topology which is why specialised apps that focus on this problem exist. 

If you wanna stick to clean topology from the get go then I advise to avoid using booleans. Booleans are more suitable for models where good topology does not matter or models that it matters a lot and they will retopologised later on.